Earth's sea ice packs are key players in the climate system and critical
indicators of climate change, as evidenced by the recent precipitous losses of
summer Arctic sea ice. As a material, frozen sea water is a polycrystalline
composite of a pure ice matrix containing brine inclusions - the melt phase -
whose volume fraction and connectivity depend strongly on temperature. The brine
phase undergoes a percolation threshold at a critical temperature where the
inclusions coalesce to form channels through which the melt phase can flow.
Fluid transport through sea ice mediates key climatological and biological
processes, and can enhance thermal transport via convection in the porous
microstructure.

During the Arctic melt season, the sea ice surface is transformed from vast
expanses of snow covered ice to complex mosaics of ice and melt ponds. Sea ice
albedo, a key parameter in climate modeling, is largely determined by melt pond
evolution. As the ponds grow and coalesce, the melt phase undergoes a
percolation threshold and the fractal dimension of the pond boundaries
transitions from 1 to about 2 around a critical pond size. In the two lectures, I will discuss mathematical models of composite
materials and statistical physics that we have been using to describe the
effective fluid, thermal, and electromagnetic transport properties of sea ice,
and to address other problems in sea ice physics such as melt pond evolution. I
will cover a range of mathematical techniques, some of which may possibly shed
light on similar questions for partially molten rock. They include percolation
theory, multiscale homogenization, integral representations for effective
transport coefficients of composite media, spectral measures and random matrix
theory, homogenization for advection diffusion processes, and Ising models.
These models have been developed in conjunction with our field experiments in
the Arctic and Antarctic. A short video on a recent Antarctic expedition will be
shown.

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